1. Practice visualizing the spirals on pinecones, seed-heads, broccoli and pineapples (scroll down): look at these sites:

2. Explain how you can get the golden ratio from the Fibonacci numbers (include some examples to make it clear what you are saying).

3. For each of these sequence rules and starting numbers, tell the next 4 numbers in the sequence:

A. Rule: 2D_n + D_n+1 = D_n+2 ; Starting numbers: D₁= 3 and D₂= 1

3, 1, ___, ____, ____...

B. Rule: E_n + 2E_n+1 = E_n+2 ; Starting numbers: E₁= 3 and E₂= 1

3, 1, ___, ___, ___ ...

C. Rule: 3F_n + 2F_n+1 = F_n+2; Starting numbers: F₁= 3 and F₂= 2

3, 2, ___, ____, ____, ...

Answers